Angles 11 plus

Olivia opens up an envelope and lays it flat, as shown below. The envelope is made from a triangle and a rectangle. What is the size of the shaded angle?

• 130°

• 135°

• 140°

• 40°

• 90°

Answer explanation

Angles in a triangle add up to 180°, so the missing angle in the triangle is 180° − 100° − 40° = 40°. All of the angles in a rectangle are right angles (90°), so the shaded angle is 90° + 40° = 130°.

What is the missing angle in this shape?

• 134°

• 98°

• 121°

• 108°

• 118°

Answer explanation

Angles in a quadrilateral add up to 360°, so the missing angle is 360° − 90° − 76° − 86° = 108

The sum of the angles inside a regular octagon is 1080°. What is the size of each angle?

• 105°

• 120°

• 180°

• 135°

• 125°

Answer explanation

A regular octagon has 8 equal angles, so each angle must be 1080° ÷ 8 = 135°.

Romesh is facing south-west. He turns clockwise until he is facing east. How many degrees clockwise does he turn through?

• 310°

• 245°

• 225°

• 180°

• 135°

Answer explanation

The angle between south‑west and west is 45°. Angles on a straight line (between west and east) add up to 180°, so he turns 45° + 180° = 225° clockwise.

What is the size of angle w?

• 225°

• 135°

• 115°

• 45°

• 120°

Answer explanation

Angles around a point add up to 360°, so angle w is 360° − 65° − 90° − 70° = 135°.

Hamza cuts a pizza into 6 equal slices. What is the size of angle x?

• 360°

• 60°

• 30°

• 90°

• 45°

Answer explanation

Angles around a point add up to 360°. The angles around the point are all equal, so x = 360° ÷ 6 = 60°.

Rhys drew the diagram below, but he only measured three of the angles. What is the size of angle g in his diagram?

• 65°

• 115°

• 70°

• 85°

• 60°

Answer explanation

Angles in a quadrilateral add up to 360°, so the missing angle in the quadrilateral is 360° − 80° − 95° − 70° = 115°. This angle is on a straight line with angle g. Angles on a straight line add up to 180°, so angle g = 180° − 115° = 65°.

Five identical angles lie on a straight line. What is the size of each angle?

• 36°

• 72°

• 24°

• 18°

• 30°

Answer explanation

Angles on a straight line add up to 180°. There are five identical angles, so each angle is 180° ÷ 5 = 36°.

Look at the diagram below. What is the value of h?

• 55°

• 165°

• 71°

• 110°

• 48°

Answer explanation

Angles around a point add up to 360°, so 114° + h + 81° + 2h = 360°. That means 3h = 360° − 114° − 81° = 165°, so h = 165° ÷ 3 = 55°.

This diagram shows a triangular coat hanger. What is the size of angle a inside the coat hanger?

• 96°

• 64°

• 116°

• 112°

• 148°

Answer explanation

Angles in a triangle add up to 180°, so a = 180° − 32° − 32° = 116°.